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hmf_forms • Show schema
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{'deg': 3, 'dimension': 1, 'disc': 733, 'field_bad_primes': [733], 'field_label': '3.3.733.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.733.1-5.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [5], 'level_ideal': '[5, 5, -w + 3]', 'level_label': '5.1', 'level_norm': 5, 'parallel_weight': 2, 'short_label': '5.1-a', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[5, 5, -w + 3]', 1]], 'hecke_eigenvalues': [0, -1, -1, -1, -3, 2, 3, -1, 7, -3, -10, -13, -4, 12, 8, 5, -7, -18, -15, -6, -18, -10, -12, -4, -3, -10, -7, 14, 8, 15, -3, 0, -13, -4, 20, -10, 2, -1, -4, -18, -12, 15, 14, 2, 20, -19, -16, -12, -3, 15, 8, 12, 6, 12, -21, 27, 8, 26, 3, -4, 0, 30, -12, -12, -18, -25, 20, 26, 26, 26, 0, -1, -19, -36, -18, 6, 17, -25, -22, -10, 3, 35, 8, -10, -25, 33, -6, -28, 6, 36, -12, 12, 11, -6, -33, -16, -10, -28, -6, 18, 0, 12, 20, -10, -30, 36, 18, -36, -16, 8, 32, 32, -3, 20, 5, -30, -12, 15, -10, -46, 36, 12, -46, 9, -42, -36, 2, -31, 14, -25, 32, 2, 51, -22, 0, 48, 39, -15, -24, -30, 48, 38, 18, 5, 33, 2, 0, 32, 5, 14, -36, -16, -6, -6, 39, 6], 'hecke_polynomial': 'x', 'label': '3.3.733.1-5.1-a'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 733, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 2]', '[4, 2, -w^2 - w + 5]', '[4, 4, w^2 + w - 4]', '[5, 5, -w + 3]', '[7, 7, -w^2 - 2*w + 3]', '[8, 2, 2]', '[8, 8, -w]', '[10, 10, -w - 2]', '[11, 11, -w^2 + 5]', '[13, 13, w + 1]', '[14, 14, w^2 + w - 6]', '[16, 4, -2*w + 4]', '[16, 4, w^2 - w - 3]', '[16, 16, w^2 + w - 8]', '[20, 10, -w^2 - w + 7]', '[20, 20, w^2 - 4]', '[22, 22, -w^2 + 2*w + 2]', '[23, 23, w^2 - 3]', '[25, 5, w^2 + 2*w - 1]', '[25, 25, w^2 + 2*w - 5]', '[26, 26, -w^2 + w + 2]', '[27, 3, -3]', '[28, 14, -w^2 + w + 5]', '[28, 28, w - 4]', '[29, 29, -3*w + 7]', '[32, 4, -2*w^2 - 2*w + 10]', '[32, 8, 2*w^2 + 2*w - 8]', '[32, 32, -2*w^2 - 3*w + 8]', '[35, 35, w^2 - 9]', '[40, 10, -2*w + 6]', '[40, 40, w^2 - 3*w]', '[43, 43, -3*w^2 - 2*w + 17]', '[44, 22, w^2 + w - 1]', '[44, 44, -w - 4]', '[46, 46, w^2 + w - 10]', '[49, 7, -2*w^2 + w + 11]', '[49, 49, 2*w^2 - 11]', '[50, 10, -w^2 - 2*w + 6]', '[50, 50, w^2 - w - 6]', '[52, 26, -3*w^2 - 3*w + 13]', '[52, 52, 3*w^2 + 4*w - 12]', '[54, 6, 3*w - 6]', '[55, 55, -2*w^2 - 4*w + 5]', '[56, 14, -2*w^2 - 4*w + 6]', '[56, 56, w^2 + 3*w]', '[58, 58, 2*w^2 + w - 10]', '[64, 4, 4]', '[64, 8, w^2 - w - 7]', '[64, 16, -2*w]', '[64, 64, -w^2 + w + 8]', '[65, 65, -w^2 + 2*w + 3]', '[67, 67, -2*w^2 - 4*w + 3]', '[70, 70, w^2 + 2*w - 10]', '[71, 71, -2*w^2 + w + 9]', '[73, 73, w^2 + 2*w - 7]', '[73, 73, -2*w^2 - 2*w + 11]', '[73, 73, w - 5]', '[77, 77, 2*w^2 + 3*w - 9]', '[80, 20, -2*w - 4]', '[80, 20, w^2 + 3*w - 3]', '[80, 80, w^2 + 2*w]', '[86, 86, -w^2 + 10]', '[88, 22, -2*w^2 + 10]', '[88, 88, w^2 + 2*w - 8]', '[89, 89, 2*w^2 + w - 9]', '[89, 89, -w^2 - 2*w + 9]', '[89, 89, -2*w - 1]', '[91, 91, -4*w + 9]', '[92, 46, -w^2 - 3*w + 1]', '[92, 92, 2*w^2 + 3*w - 4]', '[98, 14, -3*w^2 + 5*w + 6]', '[98, 98, -4*w^2 - 5*w + 14]', '[100, 10, w^2 - 3*w - 1]', '[100, 20, -2*w^2 + w + 12]', '[100, 50, -w^2 - 3*w + 13]', '[100, 100, 2*w^2 - 3*w - 4]', '[101, 101, 4*w^2 + 4*w - 19]', '[103, 103, 2*w + 3]', '[104, 26, 2*w + 2]', '[104, 104, -w^2 - w]', '[107, 107, w + 5]', '[108, 6, 3*w^2 + 3*w - 15]', '[108, 12, -3*w^2 - 3*w + 12]', '[109, 109, 3*w^2 + 2*w - 15]', '[110, 110, 2*w^2 + w - 6]', '[112, 28, -w^2 - 3*w + 7]', '[112, 28, 2*w^2 + 2*w - 12]', '[112, 112, -2*w^2 - w + 8]', '[113, 113, 2*w - 7]', '[115, 115, 3*w^2 + 2*w - 23]', '[116, 58, -w^2 - w + 11]', '[116, 116, w^2 - 2*w - 4]', '[121, 11, 2*w^2 + w - 7]', '[121, 121, -2*w^2 - w + 17]', '[125, 5, 5]', '[125, 125, 3*w^2 - 17]', '[127, 127, 2*w^2 - 9]', '[127, 127, -4*w + 11]', '[127, 127, -2*w^2 + 2*w + 9]', '[128, 8, -4*w + 8]', '[128, 8, 2*w^2 - 2*w - 6]', '[128, 32, 2*w^2 + 2*w - 16]', '[128, 128, -2*w^2 + w + 8]', '[130, 130, -w^2 - 3*w - 2]', '[131, 131, 3*w^2 + 4*w - 13]', '[134, 134, 2*w^2 + 3*w - 10]', '[135, 15, 3*w - 9]', '[137, 137, -w^2 + 2*w - 3]', '[140, 70, 3*w^2 + 3*w - 11]', '[140, 140, -3*w^2 - 5*w + 12]', '[142, 142, 4*w^2 + 3*w - 22]', '[143, 143, -2*w^2 - 2*w + 13]', '[145, 145, -w^2 - 1]', '[146, 146, -w^2 + 4*w - 6]', '[146, 146, -w^2 + 7*w - 10]', '[146, 146, -w + 6]', '[149, 149, 2*w^2 - 6*w + 1]', '[151, 151, 3*w - 1]', '[154, 154, 2*w^2 - w - 14]', '[157, 157, -3*w^2 - 6*w + 7]', '[157, 157, -2*w^2 + 3*w + 3]', '[157, 157, 2*w^2 + 2*w - 15]', '[160, 20, -2*w^2 - 2*w + 14]', '[160, 40, 2*w^2 - 8]', '[160, 160, -w^2 - 3*w + 8]', '[161, 161, -4*w^2 - 4*w + 17]', '[163, 163, 3*w^2 + 2*w - 19]', '[163, 163, 4*w^2 + 5*w - 17]', '[163, 163, -5*w^2 - 6*w + 19]', '[167, 167, w^2 - 11]', '[167, 167, -3*w - 7]', '[167, 167, -w^2 - 2*w + 13]', '[169, 13, w^2 - 2*w - 5]', '[169, 169, w^2 + 2*w + 1]', '[172, 86, 3*w^2 - w - 15]', '[172, 172, -w^2 - 3*w + 12]', '[175, 35, -2*w^2 + w + 7]', '[175, 175, 2*w^2 + 2*w - 19]', '[176, 44, -2*w^2 + 4*w + 4]', '[176, 44, w^2 + 3*w - 15]', '[176, 176, 4*w^2 - w - 24]', '[178, 178, w^2 - 3*w - 2]', '[178, 178, w^2 - 6*w + 10]', '[178, 178, 2*w^2 - 3*w - 2]', '[181, 181, -2*w - 7]', '[181, 181, 2*w^2 - 7]', '[181, 181, 2*w^2 - 2*w - 5]', '[182, 182, 3*w^2 + 2*w - 14]', '[184, 46, 2*w^2 - 6]', '[184, 184, -3*w^2 - w + 16]', '[189, 21, 3*w^2 + 6*w - 9]', '[193, 193, 2*w^2 + 2*w - 3]', '[196, 14, -5*w^2 - w + 31]', '[196, 28, 3*w^2 + 2*w - 20]', '[196, 98, -w^2 - w - 1]', '[196, 196, w^2 + 4*w - 4]', '[197, 197, -4*w^2 - 7*w + 9]', '[197, 197, 2*w^2 - 2*w - 19]', '[197, 197, 2*w^2 + 3*w - 11]', '[199, 199, -6*w^2 + 37]', '[200, 10, 2*w^2 + 4*w - 2]', '[200, 40, -3*w^2 - 6*w + 8]', '[200, 50, 2*w^2 + 4*w - 10]', '[200, 200, -3*w^2 - 3*w + 16]', '[202, 202, -w - 6]', '[203, 203, 2*w^2 - 2*w - 3]', '[206, 206, -2*w^2 + w + 6]', '[208, 52, w^2 + 3*w - 11]', '[208, 52, -2*w^2 + 2*w + 4]', '[208, 208, 3*w^2 - 16]', '[214, 214, -w^2 - 3*w + 10]', '[215, 215, -4*w^2 - 2*w + 27]', '[216, 6, 6]', '[216, 24, 3*w]', '[218, 218, w^2 - 2*w - 6]', '[220, 110, -3*w^2 + w + 19]', '[220, 220, w^2 + w - 12]', '[224, 28, -2*w^2 + 2*w + 10]', '[224, 56, 2*w - 8]', '[224, 224, -w^2 + 4*w]', '[226, 226, w^2 + 4*w + 2]', '[227, 227, 2*w^2 - 3*w - 7]', '[230, 230, -3*w^2 - 4*w + 14]', '[232, 58, -6*w + 14]', '[232, 232, 3*w^2 - 7*w]', '[233, 233, w^2 + 4*w - 15]', '[242, 22, w^2 - 5*w + 2]', '[242, 242, -3*w^2 - 5*w + 6]', '[245, 35, -5*w^2 + 6*w + 17]', '[245, 245, 2*w^2 + 5*w - 3]', '[250, 10, -5*w + 10]', '[250, 250, -5*w^2 - 6*w + 18]', '[251, 251, -4*w^2 + 23]', '[253, 253, w - 7]', '[254, 254, 2*w^2 - 5*w - 2]', '[254, 254, w^2 - 2*w - 10]', '[254, 254, w^2 - 2*w - 14]', '[256, 8, -4*w^2 - 4*w + 20]', '[256, 16, 4*w^2 + 4*w - 16]', '[256, 16, 3*w^2 + 5*w - 13]', '[256, 64, -4*w^2 - 6*w + 16]', '[256, 256, 5*w^2 + 6*w - 16]', '[257, 257, w^2 - 2*w - 7]', '[260, 130, -3*w^2 - w + 15]', '[260, 260, 2*w^2 + 3*w - 12]', '[262, 262, -w^2 - 2]', '[268, 134, -w^2 + 3*w + 3]', '[268, 268, 3*w^2 - w - 20]', '[269, 269, -4*w^2 - w + 23]', '[270, 30, 3*w + 6]', '[271, 271, 2*w^2 - w - 19]', '[274, 274, -3*w^2 + 14*w - 14]', '[275, 55, -4*w^2 - 3*w + 19]', '[275, 275, -3*w - 1]', '[277, 277, -3*w^2 - 2*w + 9]', '[280, 70, 2*w^2 - 18]', '[280, 280, -w^2 + 2*w + 8]', '[281, 281, w^2 - 2*w - 9]', '[283, 283, 6*w^2 + 5*w - 31]', '[284, 142, -3*w^2 + w + 21]', '[284, 284, w^2 - 12]', '[286, 286, -3*w + 10]', '[290, 290, 3*w^2 - w - 14]', '[292, 146, -w^2 - 3*w - 3]', '[292, 146, w^2 + 5*w + 7]', '[292, 146, 3*w^2 + 3*w - 17]', '[292, 292, -3*w^2 - 2*w + 12]', '[292, 292, -3*w^2 - 7*w + 4]', '[292, 292, 2*w^2 + 5*w - 4]', '[293, 293, 2*w^2 - 2*w - 21]', '[297, 33, 3*w^2 - 15]', '[298, 298, w^2 + 2*w + 2]', '[299, 299, 2*w^2 + 4*w - 11]', '[301, 301, -4*w^2 + w + 25]', '[302, 302, -3*w^2 + 7*w - 2]', '[308, 154, -3*w^2 - 3*w + 25]', '[308, 308, 3*w^2 - 2*w - 12]', '[311, 311, -w^2 - 4*w - 1]', '[314, 314, 3*w^2 + 2*w - 10]', '[314, 314, -4*w^2 - 5*w + 18]', '[314, 314, 5*w - 14]', '[317, 317, 3*w^2 + 2*w - 11]', '[317, 317, 2*w^2 + 3*w - 13]', '[317, 317, 2*w^2 - 2*w - 11]', '[319, 319, -4*w^2 + 6*w + 11]', '[320, 20, -4*w + 12]', '[320, 40, 3*w^2 - 3*w - 13]', '[320, 80, 2*w^2 - 6*w]', '[320, 320, -3*w^2 + 2*w + 16]', '[322, 322, 3*w + 2]', '[325, 65, 4*w^2 - 2*w - 19]', '[325, 325, 4*w^2 + 4*w - 13]', '[326, 326, -w^2 - w - 2]', '[326, 326, w^2 + 4*w - 2]', '[326, 326, w^2 + 2*w - 14]', '[331, 331, 4*w^2 - w - 21]', '[331, 331, 3*w + 5]', '[331, 331, 4*w^2 + 2*w - 21]', '[334, 334, 3*w^2 + w - 14]', '[334, 334, w^2 + 4*w - 14]', '[334, 334, w^2 - 3*w - 14]', '[335, 335, -w - 7]', '[337, 337, -2*w^2 + 4*w + 5]', '[338, 26, 3*w^2 - 6*w - 2]', '[338, 338, -w^2 - 4*w + 10]', '[343, 7, 7]', '[343, 343, -3*w^2 - 4*w + 15]', '[344, 86, -6*w^2 - 4*w + 34]', '[344, 344, 5*w^2 + 4*w - 24]', '[349, 349, w^2 - 4*w - 1]', '[350, 70, 6*w^2 + 7*w - 26]', '[350, 350, 2*w^2 + 3*w - 2]', '[351, 39, -3*w - 3]', '[352, 44, 2*w^2 + 2*w - 2]', '[352, 88, -2*w - 8]', '[352, 352, w^2 + 4*w]', '[353, 353, -w^2 - 4*w - 5]', '[355, 355, -w^2 - 4*w + 1]', '[356, 178, -w^2 - 5*w - 5]', '[356, 178, -w^2 + w + 13]', '[356, 178, 5*w^2 + 5*w - 21]', '[356, 356, 3*w^2 + 6*w - 4]', '[356, 356, -3*w - 4]', '[356, 356, -5*w^2 - 7*w + 20]', '[362, 362, 2*w^2 + 3*w - 14]', '[362, 362, 2*w^2 - 7*w + 2]', '[362, 362, -5*w^2 - 6*w + 22]', '[364, 182, -w^2 - w + 13]', '[364, 364, w^2 - 3*w - 4]', '[365, 365, -2*w^2 - 3*w + 17]', '[365, 365, -w^2 + 8*w - 15]', '[365, 365, 6*w - 13]', '[367, 367, 6*w^2 + 7*w - 23]', '[368, 92, 2*w^2 + 2*w - 20]', '[368, 92, w^2 - 5*w + 9]', '[368, 368, -2*w^2 + 3*w + 8]', '[377, 377, -3*w^2 + 4*w + 7]', '[378, 42, -3*w^2 - 3*w + 18]', '[379, 379, 2*w - 9]', '[385, 385, w^2 + 4*w - 11]', '[386, 386, -7*w + 10]', '[389, 389, 2*w^2 + 3*w - 15]', '[389, 389, w^2 + 4*w - 13]', '[389, 389, 2*w^2 + 4*w - 1]', '[392, 14, -4*w^2 + 2*w + 22]', '[392, 56, w^2 + 3*w - 16]', '[392, 98, 4*w^2 - 22]', '[392, 392, -2*w^2 - 3*w + 16]', '[394, 394, 4*w^2 + w - 22]', '[394, 394, 3*w^2 + 5*w - 14]', '[394, 394, -w^2 + 3*w - 6]', '[397, 397, 4*w - 1]', '[398, 398, 4*w^2 + 3*w - 18]', '[400, 20, -2*w^2 - 4*w + 12]', '[400, 20, 3*w^2 + w - 13]', '[400, 80, 4*w^2 + 3*w - 24]', '[400, 100, -3*w^2 - w + 25]', '[400, 100, 2*w^2 - 2*w - 12]', '[400, 400, -w + 8]', '[404, 202, -3*w^2 + w + 13]', '[404, 404, w^2 + 4*w - 12]', '[406, 406, w^2 + 4*w - 18]', '[409, 409, 2*w^2 + w - 19]', '[409, 409, -w^2 + 6*w - 11]', '[409, 409, 2*w^2 + 4*w - 21]', '[412, 206, -w^2 + 7*w - 13]', '[412, 412, -3*w^2 + 10*w - 4]', '[416, 52, -6*w^2 - 6*w + 26]', '[416, 104, 6*w^2 + 8*w - 24]', '[416, 416, 3*w^2 - 5*w - 8]', '[419, 419, 4*w^2 + 4*w - 21]', '[421, 421, -w^2 - 3]', '[421, 421, -4*w^2 - 6*w + 17]', '[421, 421, 4*w^2 + 3*w - 31]', '[428, 214, 3*w^2 - 7*w - 3]', '[428, 428, 2*w^2 - 9*w + 12]', '[430, 430, -2*w^2 - 3*w + 22]', '[432, 12, 6*w - 12]', '[432, 12, -3*w^2 + 3*w + 9]', '[432, 48, -3*w^2 - 3*w + 24]', '[436, 218, -w^2 - 7*w - 11]', '[436, 436, 4*w^2 + 9*w - 4]', '[439, 439, 5*w^2 - 29]', '[440, 110, -4*w^2 - 8*w + 10]', '[440, 440, 7*w - 16]', '[443, 443, w^2 - 13]', '[445, 445, 3*w^2 - 2*w - 11]', '[445, 445, 2*w^2 - 5*w - 3]', '[445, 445, -8*w + 19]', '[448, 28, -4*w^2 - 8*w + 12]', '[448, 56, 3*w^2 + 5*w - 5]', '[448, 112, 2*w^2 + 6*w]', '[448, 448, -4*w^2 - 7*w + 8]', '[449, 449, 4*w^2 - w - 27]', '[452, 226, 3*w^2 + 3*w - 19]', '[452, 452, -3*w^2 - w + 12]', '[454, 454, 3*w + 10]', '[455, 455, -2*w^2 - w + 1]', '[457, 457, 2*w^2 - 19]', '[460, 230, w^2 - 3*w - 5]', '[460, 460, w^2 - w + 4]', '[464, 116, -3*w^2 - w + 9]', '[464, 116, 4*w^2 + 2*w - 20]', '[464, 464, -3*w^2 - 4*w + 16]', '[466, 466, -3*w^2 + 16*w - 22]', '[467, 467, 4*w + 9]', '[467, 467, 3*w^2 - 2*w - 17]', '[467, 467, 2*w^2 - 2*w - 13]', '[469, 469, 3*w^2 - 13]', '[473, 473, w^2 + 2*w + 3]', '[479, 479, -w^2 + 4*w + 19]', '[484, 22, -3*w^2 - 7*w + 5]', '[484, 44, 5*w^2 + 8*w - 12]', '[484, 242, -3*w^2 - w + 11]', '[484, 484, 2*w^2 + 5*w - 12]', '[487, 487, 4*w^2 + 5*w - 19]', '[490, 70, 5*w^2 + w - 38]', '[490, 490, -3*w^2 - w + 10]', '[491, 491, 3*w - 11]', '[497, 497, 2*w^2 + 4*w - 13]', '[500, 10, -5*w^2 - 5*w + 25]', '[500, 20, 5*w^2 + 5*w - 20]', '[500, 250, -w^2 - w - 3]', '[500, 500, w^2 + 5*w - 4]', '[502, 502, -4*w^2 + 5*w + 14]', '[503, 503, 4*w^2 + 3*w - 17]', '[505, 505, 4*w^2 + 3*w - 25]', '[506, 506, 6*w^2 - w - 34]', '[508, 254, w^2 - 3*w - 13]', '[508, 254, -3*w^2 - 3*w + 23]', '[508, 254, -5*w^2 - w + 29]', '[508, 508, w^2 + 3*w + 4]', '[508, 508, 3*w^2 - w - 12]', '[508, 508, 3*w^2 + 3*w - 20]', '[511, 511, -6*w^2 - 7*w + 19]', '[511, 511, 9*w^2 + 12*w - 31]', '[511, 511, 2*w^2 + 6*w - 7]', '[512, 8, 8]', '[512, 16, 2*w^2 - 2*w - 14]', '[512, 32, -4*w]', '[512, 128, -2*w^2 + 2*w + 16]', '[512, 512, -w - 8]', '[514, 514, 3*w^2 - 4*w - 6]', '[515, 515, -2*w^2 + 3*w + 9]', '[520, 130, -2*w^2 + 4*w + 6]', '[520, 520, -w^2 + 4*w - 8]', '[523, 523, -2*w^2 - 5*w - 1]', '[524, 262, -3*w^2 + 5*w + 3]', '[524, 524, 4*w^2 - w - 20]', '[529, 23, -4*w^2 - w + 21]', '[529, 529, -2*w^2 + 2*w + 15]', '[535, 535, -w^2 - 2*w + 15]', '[536, 134, -4*w^2 - 8*w + 6]', '[536, 536, 6*w^2 + 11*w - 16]', '[538, 538, 3*w^2 - 3*w - 14]', '[539, 77, -6*w^2 - 4*w + 47]', '[539, 539, 2*w^2 - 6*w - 1]', '[540, 30, 3*w^2 + 3*w - 21]', '[540, 60, -3*w^2 + 12]', '[542, 542, 3*w^2 + 3*w - 22]', '[545, 545, 4*w^2 - 21]', '[547, 547, 5*w^2 + 4*w - 23]', '[548, 274, 3*w^2 + 5*w - 15]', '[548, 548, -4*w^2 - 3*w + 12]', '[550, 110, -w^2 + 3*w + 6]', '[550, 550, 4*w^2 + 3*w - 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23]', '[1867, 1867, -4*w^2 - 13*w - 7]', '[1868, 934, -17*w^2 - 17*w + 77]', '[1868, 934, 9*w^2 + 3*w - 53]', '[1868, 934, 9*w^2 + 5*w - 49]', '[1868, 1868, 17*w^2 + 21*w - 68]', '[1868, 1868, -6*w^2 - 5*w + 36]', '[1868, 1868, -7*w^2 - 7*w + 36]', '[1871, 1871, -6*w^2 + 4*w + 25]', '[1873, 1873, -4*w^2 + 5*w + 17]', '[1876, 938, w^2 - 5*w - 17]', '[1876, 1876, 2*w^2 + 5*w + 4]', '[1877, 1877, 10*w - 17]', '[1879, 1879, -2*w^2 - w - 3]', '[1882, 1882, 2*w^2 - 3*w - 26]', '[1883, 1883, -8*w^2 - 10*w + 35]', '[1885, 1885, -2*w^2 - 8*w + 7]', '[1890, 210, -3*w^2 - 6*w + 30]', '[1892, 946, 7*w^2 + 5*w - 59]', '[1892, 1892, -6*w^2 + 5*w + 28]', '[1894, 1894, w^2 + 5*w + 10]', '[1894, 1894, -w^2 + 12*w - 10]', '[1894, 1894, 2*w^2 - 11*w + 6]', '[1895, 1895, -2*w^2 + 15*w - 27]', '[1897, 1897, 8*w^2 - 2*w - 43]', '[1898, 1898, 5*w^2 - 10*w - 2]', '[1898, 1898, 2*w^2 - 9*w + 2]', '[1898, 1898, -w^2 + 5*w + 6]', '[1913, 1913, 2*w^2 - 4*w - 13]', '[1916, 958, 5*w^2 - 3*w - 29]', '[1916, 1916, -w^2 - 3*w + 20]', '[1917, 213, -6*w^2 + 3*w + 27]', '[1918, 1918, -2*w^2 - 7*w + 18]', '[1925, 385, -2*w^2 - 4*w + 27]', '[1925, 1925, 10*w^2 + 14*w - 27]', '[1930, 1930, -8*w^2 - 15*w + 22]', '[1931, 1931, 5*w^2 - 2*w - 21]', '[1936, 44, 2*w^2 - 10*w + 4]', '[1936, 44, w^2 - 5*w + 13]', '[1936, 176, -3*w^2 + 4*w + 16]', '[1936, 484, -6*w^2 - 10*w + 12]', '[1936, 484, 3*w^2 + 9*w - 1]', '[1936, 1936, 8*w^2 + 15*w - 24]', '[1937, 1937, -2*w^2 + 9*w - 15]', '[1939, 1939, 18*w^2 + 29*w - 61]', '[1943, 1943, 4*w^2 + 5*w - 27]', '[1945, 1945, -w^2 + 6*w + 21]', '[1945, 1945, w^2 + 10*w - 29]', '[1945, 1945, -w + 13]', '[1948, 974, -7*w^2 - 15*w + 9]', '[1948, 1948, 11*w^2 + 20*w - 28]', '[1951, 1951, 7*w^2 + 6*w - 39]', '[1958, 1958, -w^2 + 8*w - 18]', '[1958, 1958, 2*w^2 + 7*w - 26]', '[1958, 1958, -7*w^2 + 13*w + 10]', '[1960, 70, -10*w^2 + 12*w + 34]', '[1960, 280, -w^2 + 18*w - 40]', '[1960, 490, 4*w^2 + 10*w - 6]', '[1960, 1960, -7*w^2 - 11*w + 16]', '[1963, 1963, 3*w^2 + 2*w - 1]', '[1964, 982, 5*w^2 + 5*w - 31]', '[1964, 1964, -5*w^2 - 2*w + 20]', '[1967, 1967, 8*w^2 + 13*w - 19]', '[1970, 1970, 7*w^2 - 3*w - 34]', '[1970, 1970, -9*w^2 - 9*w + 38]', '[1970, 1970, w^2 + 8*w - 18]', '[1971, 219, 3*w^2 + 6*w - 21]', '[1971, 219, -6*w^2 - 6*w + 33]', '[1971, 219, 3*w - 15]', '[1973, 1973, 8*w^2 + 5*w - 41]', '[1973, 1973, -6*w - 1]', '[1973, 1973, w^2 + 8*w - 21]', '[1978, 1978, 5*w^2 + w - 22]', '[1979, 1979, 5*w^2 + 2*w - 15]', '[1979, 1979, -w^2 - 8*w + 29]', '[1979, 1979, 9*w^2 + 8*w - 41]', '[1981, 1981, 6*w^2 - 2*w - 39]', '[1985, 1985, -4*w^2 + 13*w - 3]', '[1988, 994, -3*w^2 - 7*w - 1]', '[1988, 1988, 5*w^2 + 11*w - 12]', '[1990, 1990, 5*w^2 - w - 22]', '[1991, 1991, 9*w^2 + 4*w - 51]', '[1991, 1991, w^2 + 2*w - 19]', '[1991, 1991, w^2 + 6*w - 25]', '[1999, 1999, -6*w^2 + 9*w + 13]', '[2000, 20, -10*w + 20]', '[2000, 20, 5*w^2 - 5*w - 15]', '[2000, 80, 5*w^2 + 5*w - 40]', '[2000, 500, -10*w^2 - 12*w + 36]', '[2000, 500, 9*w^2 + 11*w - 39]', '[2000, 2000, 11*w^2 + 17*w - 40]', '[2002, 2002, 3*w^2 - w - 30]', '[2008, 502, -8*w^2 + 46]', '[2008, 2008, 4*w^2 + 5*w - 32]', '[2011, 2011, 6*w^2 + 5*w - 47]', '[2011, 2011, 10*w^2 + 12*w - 43]', '[2011, 2011, 4*w^2 - 3*w - 25]', '[2012, 1006, w^2 - 13*w + 23]', '[2012, 2012, 6*w^2 - 15*w + 4]', '[2017, 2017, 6*w^2 - 31]', '[2018, 2018, 11*w^2 + 13*w - 42]', '[2020, 1010, -5*w^2 - 11*w + 13]', '[2020, 2020, w^2 + 8*w + 12]', '[2024, 506, 2*w - 14]', '[2024, 2024, -w^2 + 7*w]', '[2026, 2026, w^2 - w - 18]', '[2027, 2027, -4*w^2 + 8*w + 9]', '[2030, 2030, -4*w^2 - 7*w + 22]', '[2032, 508, 4*w^2 - 10*w - 4]', '[2032, 508, -w^2 - 7*w + 27]', '[2032, 508, w^2 + 7*w - 3]', '[2032, 508, 3*w^2 + 5*w - 1]', '[2032, 508, 2*w^2 - 4*w - 20]', '[2032, 508, 2*w^2 - 4*w - 28]', '[2032, 2032, -7*w^2 + 3*w + 40]', '[2032, 2032, w^2 + 7*w + 8]', '[2032, 2032, w^2 + 3*w + 8]', '[2038, 2038, -7*w + 2]', '[2041, 2041, -12*w^2 - 20*w + 31]', '[2041, 2041, 6*w^2 + w - 31]', '[2041, 2041, w^2 + 8*w - 19]', '[2042, 2042, w^2 + 12*w - 38]', '[2044, 1022, 5*w^2 - 3*w - 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57]', '[9944, 2486, 10*w^2 - 8*w - 38]', '[9944, 9944, -w^2 - 16*w + 40]', '[9946, 9946, 10*w^2 - 21*w - 14]', '[9947, 203, 14*w^2 + 21*w - 35]', '[9947, 9947, -10*w + 33]', '[9950, 1990, -13*w^2 + 4*w + 78]', '[9950, 9950, 11*w^2 + 22*w - 30]', '[9952, 1244, 26*w^2 + 30*w - 106]', '[9952, 2488, -28*w^2 - 38*w + 104]', '[9952, 9952, 33*w^2 + 46*w - 112]', '[9955, 9955, -8*w^2 - 14*w + 39]', '[9955, 9955, -16*w^2 - 24*w + 61]', '[9955, 9955, 26*w^2 + 46*w - 67]', '[9961, 9961, 15*w^2 - 2*w - 85]', '[9967, 9967, -2*w^2 + 7*w - 19]', '[9968, 2492, 3*w^2 - 7*w + 15]', '[9968, 2492, 9*w^2 + 3*w - 23]', '[9968, 2492, -3*w^2 - 13*w + 9]', '[9968, 2492, 4*w^2 + 2*w - 44]', '[9968, 2492, -10*w^2 - 6*w + 44]', '[9968, 2492, -2*w^2 + 8*w + 28]', '[9968, 9968, 8*w^2 + 13*w - 40]', '[9968, 9968, -3*w^2 + 8*w + 16]', '[9968, 9968, -3*w^2 - 7*w - 8]', '[9976, 2494, -4*w^2 + 14*w + 2]', '[9976, 9976, 8*w^2 - 5*w - 48]', '[9977, 9977, -15*w^2 - 10*w + 123]', '[9977, 9977, 12*w^2 + 15*w - 55]', '[9977, 9977, 4*w^2 - 8*w - 19]', '[9983, 9983, -10*w - 3]', '[9986, 9986, 8*w^2 - 15*w - 18]', '[9986, 9986, 9*w^2 - 22*w - 6]', '[9986, 9986, 10*w^2 + 3*w - 50]', '[9988, 4994, 11*w^2 + 3*w - 87]', '[9988, 9988, -7*w^2 + 5*w + 44]', '[9989, 9989, 5*w^2 - 12*w - 11]', '[9992, 2498, 8*w^2 + 2*w - 26]', '[9992, 9992, -5*w^2 - 15*w + 32]', '[9995, 9995, -w^2 - 12*w + 5]', '[9998, 9998, -9*w^2 - 5*w + 34]', '[10000, 100, -18*w^2 - 26*w + 68]', '[10000, 100, 17*w^2 + 19*w - 67]', '[10000, 100, -10*w - 20]', '[10000, 100, 5*w^2 + 15*w - 15]', '[10000, 400, -8*w^2 + 19*w + 8]', '[10000, 400, 5*w^2 + 10*w]', '[10000, 2500, -8*w^2 - 2*w + 28]', '[10000, 2500, 7*w^2 + 9*w - 45]', '[10000, 10000, 5*w^2 + 14*w - 32]'], 'label': '3.3.733.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w + 2]', '[4, 2, -w^2 - w + 5]', '[5, 5, -w + 3]', '[7, 7, -w^2 - 2*w + 3]', '[11, 11, -w^2 + 5]', '[13, 13, w + 1]', '[23, 23, w^2 - 3]', '[25, 5, w^2 + 2*w - 1]', '[27, 3, -3]', '[29, 29, -3*w + 7]', '[43, 43, -3*w^2 - 2*w + 17]', '[49, 7, -2*w^2 + w + 11]', '[67, 67, -2*w^2 - 4*w + 3]', '[71, 71, -2*w^2 + w + 9]', '[73, 73, w^2 + 2*w - 7]', '[73, 73, -2*w^2 - 2*w + 11]', '[73, 73, w - 5]', '[89, 89, 2*w^2 + w - 9]', '[89, 89, -w^2 - 2*w + 9]', '[89, 89, -2*w - 1]', '[101, 101, 4*w^2 + 4*w - 19]', '[103, 103, 2*w + 3]', '[107, 107, w + 5]', '[109, 109, 3*w^2 + 2*w - 15]', '[113, 113, 2*w - 7]', '[121, 11, 2*w^2 + w - 7]', '[127, 127, 2*w^2 - 9]', '[127, 127, -4*w + 11]', '[127, 127, -2*w^2 + 2*w + 9]', '[131, 131, 3*w^2 + 4*w - 13]', '[137, 137, -w^2 + 2*w - 3]', '[149, 149, 2*w^2 - 6*w + 1]', '[151, 151, 3*w - 1]', '[157, 157, -3*w^2 - 6*w + 7]', '[157, 157, -2*w^2 + 3*w + 3]', '[157, 157, 2*w^2 + 2*w - 15]', '[163, 163, 3*w^2 + 2*w - 19]', '[163, 163, 4*w^2 + 5*w - 17]', '[163, 163, -5*w^2 - 6*w + 19]', '[167, 167, w^2 - 11]', '[167, 167, -3*w - 7]', '[167, 167, -w^2 - 2*w + 13]', '[169, 13, w^2 - 2*w - 5]', '[181, 181, -2*w - 7]', '[181, 181, 2*w^2 - 7]', '[181, 181, 2*w^2 - 2*w - 5]', '[193, 193, 2*w^2 + 2*w - 3]', '[197, 197, -4*w^2 - 7*w + 9]', '[197, 197, 2*w^2 - 2*w - 19]', '[197, 197, 2*w^2 + 3*w - 11]', '[199, 199, -6*w^2 + 37]', '[227, 227, 2*w^2 - 3*w - 7]', '[233, 233, w^2 + 4*w - 15]', '[251, 251, -4*w^2 + 23]', '[257, 257, w^2 - 2*w - 7]', '[269, 269, -4*w^2 - w + 23]', '[271, 271, 2*w^2 - w - 19]', '[277, 277, -3*w^2 - 2*w + 9]', '[281, 281, w^2 - 2*w - 9]', '[283, 283, 6*w^2 + 5*w - 31]', '[293, 293, 2*w^2 - 2*w - 21]', '[311, 311, -w^2 - 4*w - 1]', '[317, 317, 3*w^2 + 2*w - 11]', '[317, 317, 2*w^2 + 3*w - 13]', '[317, 317, 2*w^2 - 2*w - 11]', '[331, 331, 4*w^2 - w - 21]', '[331, 331, 3*w + 5]', '[331, 331, 4*w^2 + 2*w - 21]', '[337, 337, -2*w^2 + 4*w + 5]', '[349, 349, w^2 - 4*w - 1]', '[353, 353, -w^2 - 4*w - 5]', '[367, 367, 6*w^2 + 7*w - 23]', '[379, 379, 2*w - 9]', '[389, 389, 2*w^2 + 3*w - 15]', '[389, 389, w^2 + 4*w - 13]', '[389, 389, 2*w^2 + 4*w - 1]', '[397, 397, 4*w - 1]', '[409, 409, 2*w^2 + w - 19]', '[409, 409, -w^2 + 6*w - 11]', '[409, 409, 2*w^2 + 4*w - 21]', '[419, 419, 4*w^2 + 4*w - 21]', '[421, 421, -w^2 - 3]', '[421, 421, -4*w^2 - 6*w + 17]', '[421, 421, 4*w^2 + 3*w - 31]', '[439, 439, 5*w^2 - 29]', '[443, 443, w^2 - 13]', '[449, 449, 4*w^2 - w - 27]', '[457, 457, 2*w^2 - 19]', '[467, 467, 4*w + 9]', '[467, 467, 3*w^2 - 2*w - 17]', '[467, 467, 2*w^2 - 2*w - 13]', '[479, 479, -w^2 + 4*w + 19]', '[487, 487, 4*w^2 + 5*w - 19]', '[491, 491, 3*w - 11]', '[503, 503, 4*w^2 + 3*w - 17]', '[523, 523, -2*w^2 - 5*w - 1]', '[529, 23, -4*w^2 - w + 21]', '[547, 547, 5*w^2 + 4*w - 23]', '[557, 557, 4*w^2 - 2*w - 33]', '[563, 563, 2*w^2 + 2*w - 1]', '[563, 563, 3*w^2 - 8*w - 1]', '[563, 563, 3*w^2 + 4*w - 5]', '[571, 571, 5*w^2 + 10*w - 11]', '[577, 577, -4*w + 13]', '[587, 587, 3*w^2 + 4*w - 17]', '[593, 593, 3*w^2 - 11]', '[593, 593, 4*w^2 + 2*w - 19]', '[593, 593, w - 9]', '[601, 601, -4*w^2 - 10*w + 3]', '[607, 607, 3*w^2 + 4*w - 27]', '[607, 607, -4*w^2 - 2*w + 33]', '[607, 607, 2*w^2 - 7*w + 9]', '[617, 617, -2*w^2 + 9*w - 5]', '[619, 619, -4*w - 1]', '[631, 631, -8*w^2 - 10*w + 29]', '[641, 641, w^2 - 4*w - 3]', '[653, 653, 3*w^2 - 2*w - 9]', '[659, 659, 2*w^2 + 4*w - 19]', '[661, 661, 6*w^2 + 6*w - 25]', '[673, 673, 6*w^2 + 7*w - 27]', '[683, 683, 5*w^2 + 2*w - 27]', '[701, 701, 7*w - 13]', '[709, 709, 6*w^2 + 8*w - 25]', '[719, 719, -2*w^2 + 4*w + 7]', '[719, 719, -7*w^2 - 10*w + 27]', '[719, 719, 4*w^2 - w - 19]', '[727, 727, 3*w^2 + 8*w + 1]', '[733, 733, 3*w^2 - 2*w - 7]', '[733, 733, 3*w^2 - 2*w - 29]', '[739, 739, -w - 9]', '[751, 751, -w^2 - 4*w + 19]', '[757, 757, -4*w - 7]', '[761, 761, -5*w^2 - 4*w + 29]', '[787, 787, -2*w^2 - 6*w + 3]', '[809, 809, -w^2 + 4*w - 9]', '[809, 809, -4*w^2 + 3*w + 15]', '[809, 809, 2*w^2 - 9*w + 13]', '[821, 821, -4*w^2 - 9*w + 7]', '[821, 821, 5*w - 1]', '[821, 821, 8*w^2 + 11*w - 31]', '[827, 827, 8*w^2 + 8*w - 35]', '[829, 829, 2*w^2 - 5*w - 27]', '[839, 839, -w^2 - 6*w - 7]', '[841, 29, 3*w^2 + 4*w - 31]', '[863, 863, 4*w^2 - 19]', '[883, 883, -5*w^2 + 27]', '[887, 887, 5*w^2 + 4*w - 21]', '[907, 907, -6*w^2 + 2*w + 31]', '[907, 907, 2*w^2 - 5*w - 29]', '[907, 907, 2*w^2 + 5*w - 15]', '[911, 911, w^2 - 15]', '[919, 919, 8*w - 17]', '[941, 941, -4*w^2 + 5*w + 15]', '[947, 947, 4*w^2 + 2*w - 13]', '[947, 947, 3*w^2 - 6*w - 7]', '[947, 947, -5*w^2 - 4*w + 15]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [8, -7, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 733, 'disc_rad': 733, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [[2, 1], [1, 1]]], [11, [[2, 1], [1, 1]]], [13, [[2, 1], [1, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[2, 1], [1, 1]]], [29, [[2, 1], [1, 1]]], [31, [[3, 1]]], [37, [[3, 1]]], [41, [[3, 1]]], [43, [[2, 1], [1, 1]]], [47, [[3, 1]]], [53, [[3, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3], 'galois_label': '3T2', 'galt': 2, 'grd': 27.073972741361768, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.733.1', 'local_algs': ['m733.1.1.0', 'm733.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [733], 'rd': 9.01643088997, 'regulator': {'__RealLiteral__': 0, 'data': '5.30908411022', 'prec': 44}, 'res': {'gal': ['-1,-2,26,0,-26,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( 2 a - 5 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}